To solve the problem, we need to identify the pattern or rule governing the relationship between the numbers and the shapes in the image. Let's analyze the given information step by step.
Step 1: Understand the Structure
The image shows a circular arrangement with:
-
Numbers placed at the vertices of the circle.
-
Shapes (squares) placed along the edges of the circle.
- One number (18) is already filled in one of the squares.
The numbers at the vertices are:
4, 5, 8, 6, 2.
Step 2: Identify the Pattern
We need to determine how the numbers in the squares relate to the numbers at the vertices. Let's denote the vertices as follows:
- Top: 5
- Top-left: 4
- Bottom-left: 6
- Bottom-right: 2
- Top-right: 8
The squares are positioned between these vertices. We need to find a consistent rule that applies to all squares.
Step 3: Analyze the Given Square (18)
The square labeled "18" is located between the vertices labeled "8" and "2". This suggests that the number in each square might be derived from the two adjacent vertex numbers.
#### Hypothesis: Multiplication
Let's test if the number in each square is the product of the two adjacent vertex numbers:
- For the square labeled "18":
\[
8 \times 2 = 18
\]
This matches the given value.
Step 4: Apply the Rule to Other Squares
Now, let's apply the multiplication rule to the other squares:
1.
Square between 4 and 5:
\[
4 \times 5 = 20
\]
2.
Square between 5 and 8:
\[
5 \times 8 = 40
\]
3.
Square between 8 and 6:
\[
8 \times 6 = 48
\]
4.
Square between 6 and 2:
\[
6 \times 2 = 12
\]
Step 5: Verify the Solution
The multiplication rule consistently produces the values for all squares:
- Between 4 and 5: 20
- Between 5 and 8: 40
- Between 8 and 6: 48
- Between 6 and 2: 12
- Between 2 and 8: 18 (already given)
Final Answer
The numbers in the squares are:
\[
\boxed{20, 40, 48, 12}
\]
Parent Tip: Review the logic above to help your child master the concept of magic hexagon worksheet.
